{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,27]],"date-time":"2025-02-27T05:32:07Z","timestamp":1740634327748,"version":"3.38.0"},"reference-count":22,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Commun. Contemp. Math."],"published-print":{"date-parts":[[2010,10]]},"abstract":"<jats:p>In this paper, we study minimax Aubry\u2013Mather measures and its main properties. We consider first the discrete time problem and then the continuous time case. In the discrete time problem, we establish existence, study some of the main properties using duality theory and present some examples. In the continuous time case, we establish both existence and non-existence results. First, we give some examples showing that in continuous time stationary minimax Mather measures are either trivial or fail to exist. A more natural definition in continuous time are T-periodic minimax Mather measures. We give a complete characterization of these measures and discuss several examples.<\/jats:p>","DOI":"10.1142\/s0219199710004019","type":"journal-article","created":{"date-parts":[[2010,10,20]],"date-time":"2010-10-20T12:10:12Z","timestamp":1287576612000},"page":"789-813","source":"Crossref","is-referenced-by-count":1,"title":["MINIMAX PROBABILITIES FOR AUBRY\u2013MATHER PROBLEMS"],"prefix":"10.1142","volume":"12","author":[{"given":"DIOGO A.","family":"GOMES","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal"}]},{"given":"NARA","family":"JUNG","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Toronto, Bahen Centre, 40 St. George St., Toronto, Ontario, M5S 2E4, Canada"}]},{"given":"ARTUR O.","family":"LOPES","sequence":"additional","affiliation":[{"name":"Instituto de Matem\u00e1tica, Universidade Federal do Rio Grande do Sul, Av. Bento Gon\u00e7alves, 9500, 91509-900, Porto Alegre, RS, Brazil"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"633","volume":"11","author":"Francesca A.","journal-title":"ESAIM Control Optim. Calc. Var."},{"volume-title":"Gradient Flows in Metric Spaces and in the Space of Probability Measures","year":"2005","author":"Ambrosio L.","key":"rf2"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1080\/03605300500299992"},{"journal-title":"S\u00e3o Paulo J. Math. 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